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Question
Find the sum of the following arithmetic series:
`7 + 10 1/2 + 14 + ....... + 84`
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Solution
The given arithmetic series is `7 + 10 1/2 + 14 + ....... + 84`
` Here , a = 7 , d = 10 1/2 - 7 = 21/ 2 - 7 = (21-4)/2 = 7/2 and l = 84.`
Let the given series contains n terms. Then,
an = 84
`⇒ 7 + (n-1) xx 7/2 = 84 [ a_n = a + (n-1) d ]`
` ⇒ 7/2 n + 7/2 = 84`
`⇒ 7/2 n = 84 - 7/2 = 161/2`
`⇒ n = 161/7 = 23`
∴ Required sum`= 23/2 xx (7 + 84) [ s_n = n/2 (a+l) ]`
`=23/2 xx 91`
=`2030/2`
`1046 1/2`
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